No. Some parents like the convenience, but it's definitely not necessary. Babies are often sleeping in the same room as their parents for the first few months, so a baby monitor is not needed at night. The monitors are not protective for the baby (we've had healthy babies for a lot longer than we've had baby monitors), they just allow the parent a measure of comfort if they are in a separate room.
No. My mother didn't have one, neither did either of my grandmothers nor any of my great grandmothers. You get the idea.